- CFA Exams
- CFA Exam: Level II 2021
- Study Session 14. Derivatives
- Reading 38. Valuation of Contingent Claims
- Subject 5. Black Option Valuation Model

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**CFA Practice Question**

A forward contract is priced at $129. A European option on the forward contract has an exercise price of $135 and expires in 49 days. The continuously compounded risk-free rate is 3.75% and volatility is 0.25. Calculate the prices of a call option and a put option on the forward contract.

Correct Answer: 2.3229 and 8.2927

d

d

N(d

N(d

p = e

First calculate T: T = 49/365 = 0.1342.

Then calculate the values of d

_{1}and d_{2}.d

_{1}= [ln(129/135) + (0.25)^{2}/2 x 0.1342] / (0.25 x 0.1342^{1/2}) = -0.4505d

_{2}= -0.4505 - 0.25 x 0.1342^{1/2}= -0.5421Using the normal distribution table,

N(d

_{1}) = N(-0.4505) = 1 - N(0.4505) = 1 - 0.6736 = 0.3264N(d

_{2}) = N(-0.5421) = 1 - N(0.5421) = 1 - 0.7054 = 0.2946c = e

^{-0.0375 x 0.1342}(129 x 0.3264 - 135 x 0.2946) = 2.3229p = e

^{-0.0375 x 0.1342}[135 x (1 - 0.2946) - 129 x (1 - 0.3264)] = 8.2927###
**User Contributed Comments**
4

User |
Comment |
---|---|

danlan2 |
129 is the future price. |

NIKKIZ |
It seems to me that there's a bit missing from the calculation of N(d1). I think it should be: {ln(129/135)+[0.0375+(0.25^2/2)]0.13425}/[0.25 X 0.13425^0.5]. The answer would be -0.39553. Am I missing something? |

Greatrussian |
NIKKIZ: The risk free rate 0.0375 should not be used in the calculation of d1. |

maxsouto |
NIKKIZ: The value of an option can't be less than 0 |